This paper applies the Sobol’ decomposition of a function of many random variables to a problem in structural mechanics, namely the collapse of a two story two bay frame under gravity load. Prior to introduction of this example application, the Sobol’ decomposition itself is reviewed and extended to cover the case in which the input random variables have Gaussian distribution. Then, an illustra...

A new method for estimating Sobol’ indices is proposed. The new method makes use of 3 independent input vectors rather than the usual 2. It attains much greater accuracy on problems where the target Sobol’ index is small, even outperforming some oracles which adjust using the true but unknown mean of the function. When the target Sobol’ index is quite large, the oracles do better than the new m...

In this paper we propose a mechanism for enhancing the performance of the Artificial Bee Colony Algorithm (ABCA) by making use low discrepancy Sobol sequence. The performance of the proposed Sobol sequence guided ABC (S-ABC) is analyzed over several benchmark functions and also compared to that of basic ABC. The empirical results show that the presence of low discrepancy sequence like that of S...

The estimation of variance-based importance measures (called Sobol’ indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for high-dimensional model involving a large number of input variables (typically more than ten). Recently, Sobol and Kucherenko have proposed the Derivative-based Global Sensitivity Measures (DGSM),...

Sensitivity analysis has been widely used for rational decision making of energy retrofit alternatives. A Sobol method is a variance based approach and provides powerful post-processing sensitivity results that enable to quantitatively identify influential and non-influential inputs. It can account for impacts of each input as well as impacts caused by all possible interactions between each inp...

Sobol indices are a widespread quantitative measure for variance-based global sensitivity analysis, but computing and utilizing them remains challenging for high-dimensional systems. We propose the tensor train decomposition (TT) as a unified framework for surrogate modeling and global sensitivity analysis via Sobol indices. We first overview several strategies to build a TT surrogate of the un...

This paper presents a new mutation operator called the Sobol Mutation (SOM) operator for enhancing the performance of Quantum Particle Swarm Optimization (QPSO) algorithm. The SOM operator unlike most of its contemporary mutation operators do not use the random probability distribution for perturbing the swarm population, but uses a quasi random Sobol sequence to find new solution vectors in th...

Direction numbers for generating Sobol′ sequences that satisfy the so-called Property A in up to 1111 dimensions have previously been given in Joe and Kuo [ACM Trans. Math. Software, 29 (2003), pp. 49–57]. However, these Sobol′ sequences may have poor two-dimensional projections. Here we provide a new set of direction numbers alleviating this problem. These are obtained by treating Sobol′ seque...

High-dimensional integrals are usually solved with Monte Carlo algorithms although theory suggests that low discrepancy algorithms are sometimes superior. We report on numerical testing which compares low discrepancy and Monte Carlo algorithms on the evaluation of nancial derivatives. The testing is performed on a Collateralized Mortgage Obligation (CMO) which is formulated as the computation o...

Global sensitivity analysis of a numerical code, more specifically estimation of Sobol indices associated with input variables, generally requires a large number of model runs. When those demand too much computation time, it is necessary to use a reduced model (metamodel) to perform sensitivity analysis, whose outputs are numerically close to the ones of the original model, while being much fas...